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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The monodromy of meromorphic projective structures


Authors: Dylan G. L. Allegretti and Tom Bridgeland
Journal: Trans. Amer. Math. Soc. 373 (2020), 6321-6367
MSC (2010): Primary 30F30, 34M40, 57M50; Secondary 13F60, 18E30, 34M60
DOI: https://doi.org/10.1090/tran/8093
Published electronically: June 24, 2020
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Abstract: We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $ \operatorname {PGL}_2(\mathbb{C})$ local systems on the associated marked bordered surface. We prove that the image of this map is contained in the union of the domains of the cluster charts. We discuss a number of open questions concerning this monodromy map.


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Additional Information

Dylan G. L. Allegretti
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
MR Author ID: 1189385

Tom Bridgeland
Affiliation: School of Mathematics and Statistics, University of Sheffield, Western Bank, Sheffield, S10 2TN United Kingdom

DOI: https://doi.org/10.1090/tran/8093
Received by editor(s): March 18, 2019
Received by editor(s) in revised form: January 1, 2020
Published electronically: June 24, 2020
Article copyright: © Copyright 2020 American Mathematical Society